My colleague and I work together on a project. We generally get along well on a personal level, and he makes good contributions to the team. His opinions are often valuable and highlight things we might not have thought of.
Recently we've started butting heads. Basically, if he can't see why a certain decision is made or has an idea in his head, then he just won't let it go until every angle has been debated. It gets to the point where it's easier to give up and let him have his way just so we can get on with things. That's not to say we never compromise, but the times when he digs in are getting more frequent.
I've written two examples below, but I've observed similar behaviour in discussions that I haven't been involved in. [Edit: I've removed the examples because too many answers are focusing on the details of those and not the bolded questions. If you want to see what they were, check the edit history]
This is wasting a lot of time, especially so when it relates to things that are already done/decided. His responses get to the point where he sounds sulky - "do as you see fit", etc. - but even then he won't drop it. If we do it his way, it could mean throwing away other work or compromising on something already completed just for the sake of appeasement.
We work very closely together, so it's important to maintain a positive working relationship, but his stubbornness and taking things personally are making me avoid engaging him in case it turns into a long, draining argument. The most recent argument has left me in a bad mood for days and unable to focus on my work.
For various reasons, we don't have a clear management structure, so it's hard for me to bring it up with anyone who has authority without it looking like a big escalation. We both started our roles at the same time (less than a year ago) and are at the same level, but from our previous positions, he would have been quite a bit more senior to me. That said, the main part of our work is outside our areas of expertise, so we're both relatively new.
For the short term, what can I do to complete my work in situations where it looks like he's digging in? For the longer term, what can I do to discourage this behaviour without damaging the working relationship?